Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

Given that \(3{{x}^{3}}+5{{x}^{2}}-4x-6\equiv \left( 3x+A \right)\left( x-1 \right)\left( x+4 \right)+B\left( x-1 \right)+C\) for all values of \(x\).

1. Find the values of \(A\), \(B\), and \(C\).
2. Hence, deduce the remainder when \(3{{x}^{3}}+5{{x}^{2}}-4x-6\) is divided by \({{x}^{2}}+3x-4\).